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Appendix IL                             845

weakened at the half cross-section be.     Thus only about half
the usual bolt strength is required.

Equating the strengths of shaft and bolts, and neglecting the
small half cross-sectional bolt strength at <,

D3

The number of bolts may be X = 2 '5 J D

the nearest whole number being taken. If also the ring c be
made large enough to cover the bolt washers, it will have ample
strength.

P. 426. Deflection of Helical Springs.  In his difficult
and laborious investigations on the strength of square and
rectangular shafts, St Venant found that the greatest stress and
strain occurred at the middle of the (longest) side of the sections.
Now in formula for 0, p. 424, d is evidently the diameter of
greatest stress; therefore, for square wire,

wr                     , A       zs r             ,.

60'5

O

while for rectangular wire (see p. 421),

and A =          =                42.6

c*          ** *

P. 430-2: Moment of Resistance, Moment of Inertia
or Second Moment, and Centres of Gravity.  As area

has no mass, purists now object to the term * Moment of Inertia
of Area/ substituting the more reasonable ' Second Moment / and
* Centroid* is similarly adopted instead of 'Centre of Gravity of
Area.' Also we may define the nth moment of an area round a
given line, as that obtained by dividing the area into very small
pieces, and multiplying every piece by the nth power of its
distance from the given line ; or, algebraically,

nih moment = 2 (ahn)